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Course Profile
Mathematics of Personal Finance, Grade 11, College Preparation, Catholic
and Public
Course Overview
Course
Profiles are professional development materials designed to help teachers
implement the new Grade 11 secondary school curriculum. These materials were
created by writing partnerships of school boards and subject associations. The
development of these resources was funded by the Ontario Ministry of Education.
This document reflects the views of the developers and not necessarily those of
the Ministry. Permission is given to reproduce these materials for any purpose
except profit. Teachers are also encouraged to amend, revise, edit, cut, paste,
and otherwise adapt this material for educational purposes.
Any
references in this document to particular commercial resources, learning
materials, equipment, or technology reflect only the opinions of the writers of
this sample Course Profile, and do not reflect any official endorsement by the
Ministry of Education or by the Partnership of School Boards that supported the
production of the document.
© Queen’s
Printer for Ontario, 2001
Public
and Catholic District School Board Writing Teams – Mathematics of Personal
Finance
Public
Project Manager
Karen
Allan – Durham District Board of Education
Co-lead
Writers
Krysta
Mehler – Greater Essex County District School Board
Jeff
Brosseau – Greater Essex County District School Board
Writer
Ken
O’Neill – Kawartha Pine-Ridge District School Board
Reviewers
Peter
Stasiuk – Durham College
Steve
Etienne – Niagara District School Board
Shirley
Scott – Niagara District School Board
Gail
Ivanco – Durham District School Board
Catholic
Project Manager
Barry
Elliott – Windsor-Essex Catholic District School Board
Lead
Writer
Susan
Di Laudo – Windsor-Essex Catholic District School Board
Writing
Team
Anne
Hebert – Windsor-Essex Catholic District School Board
John
Basarac – Windsor-Essex Catholic District School Board
Reviewers
Bernie
Masromattei, Special Education Consultant – Windsor-Essex Catholic District
School Board
Fr.
Peter Hrytsyk, Catholic Studies Chairperson, Holy Names High School – Windsor
Frank
Stranges, Mathematics Teacher, John Paul II Secondary School – London
Dave
Davis, Mathematics Coordinator, St. Clair College – Windsor
Dr.
Richard Caron, Dean of Mathematics and Science – University of Windsor
Course
Overview
Mathematics
of Personal Finance, Grade 11, College Preparation, MBF3C
This
course promotes the development of problem-solving and decision-making skills
in a realistic financial context. The concepts of exponential growth, sequences,
and series are studied. These concepts are explored through the concrete
applications of interest, investments, living accommodation, transportation,
and budgets. The financial framework of the course utilizes individual career
paths and projected incomes established using each student’s Annual Education
Plan (AEP). Course activities incorporate the technological tools appropriate
for financial analysis. Upon successful completion of the course, students will
have the skills necessary to make sound financial decisions in both
post-secondary endeavours and personal life situations.
This
course encourages the Catholic learner to develop his/her gifts and abilities
to promote growth toward personal responsibility in preparation for a chosen
career path. Throughout the course, emphasis should be placed on moral,
ethical, and realistic decision-making in an effort to build responsible
citizenship. The classroom environment should instill a spirit of cooperation,
rather than competition amongst students, and should foster a collaborative
sense of community. The course provides many opportunities for students to work
effectively as interdependent team members and to acknowledge and respect the
opinions of others.
Students
in this course benefit from the following:
Emphasis
should be placed on developing students’ decision-making skills in a realistic
framework. This can be initiated in Unit 1 through an exploration of career
opportunities and prospective incomes. This career investigation should be
individualized and consistent with each student’s AEP, as developed in the
Teacher Advisor Program. Making a connection between career paths and the
curriculum fosters student interest and provides them with a context for course
concepts.
Society
demands that people be proficient in the use of a variety of technological
tools. As such, the integration of technology is a critical aspect of this
course and should be used wherever applicable. The technological tools
appropriate for the students of this course include: scientific calculators, graphing calculators,
spreadsheet software, budgeting software, and the Internet. The proper use of
technology can reinforce student understanding and facilitates problem solving.
The basis
of financial planning is the ability to make informed decisions that can be
justified using mathematical reasoning. Students should be encouraged to
communicate and support their decisions with the use of appropriate
mathematical tools. Teachers should provide the opportunity for students to
make financial choices based on real-life scenarios to better prepare students
for their financial futures.
The
organization of this course fosters a logical progression of concepts for the
student. In Unit 1, the investigation of realistic incomes related to chosen
career paths captures student interest and creates a more personal learning
environment. Projected incomes from Unit 1 can be integrated into a study of
basic savings options and the mathematics of interest in Unit 2. The
mathematics of financial growth investigated in Unit 3 will be applied to
investment strategies in Unit 4. The financial implications of living
accommodation and transportation costs are studied in Units 5 and 6. The impact
of various factors on personal household budgets is examined in Unit 7. In Unit
8, students apply their knowledge of previously learned concepts to the
creation of a comprehensive long-term financial plan reflective of the career
path chosen in unit one.
|
Unit 1 |
Investigating Income Opportunities |
6 hours |
|
Unit 2 |
It’s of INTEREST to You |
14 hours |
|
Unit 3 |
The Mathematics of Financial Growth |
16 hours |
|
Unit 4 |
Sequences and Series and their Financial Applications |
20 hours |
|
* Unit 5 |
Home Sweet Home |
20 hours |
|
Unit 6 |
Getting Behind the Wheel |
10 hours |
|
* Unit 7 |
Managing Your Money |
17 hours |
|
Unit 8 |
Summative: Planning your Financial Future |
7 hours |
* These
units are fully developed in this Course Profile.
Time: 6 hours
Unit
Description
Students
explore a variety of occupations of personal interest that are attainable
through their chosen educational path. Expected incomes and
educational/training costs involved for their careers of choice are researched
and analysed. This topic provides a vehicle for the teacher to review such
mathematical concepts as data management, trend analysis, and approaches to
problem-solving. Students investigate occupations projected to be in high
demand and the educational paths required to enter these fields. It is
recommended that students use the anticipated income from one or two potential
careers as a focus for the course. This forms the framework for investigations
in the remaining units on such topics as affordable mortgages, investment
opportunities, and personal budgeting.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
PFV.05, PF5.01, PF5.02, PF5.03 CGE2c, CGE4f, CGE4g, CGE5b |
Knowledge/Understanding Communication Thinking/Inquiry/Problem Solving |
Investigate Careers and Income Potential |
Time: 14 hours
Unit
Description
Students
expand their knowledge of various savings options offered by financial
institutions. Simple interest and compound interest are explored in the context
of savings plans, with and without the use of technology. An understanding of
compounding is used to examine the nature of exponential growth. Students
describe the significance of exponential growth as represented by tables,
graphs, and equations. Models of exponential functions are provided to allow
the students to apply their knowledge. Students use their acquired knowledge
and their chosen career path to make decisions about realistic savings
alternatives and justify these decisions mathematically.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
PFV.04, CIV.03, PF4.01, PF4.02, CI3.01 CGE2b |
Knowledge/Understanding Communication Application |
Comparing Types of Savings Options |
|
2 |
CIV.02, CIV.03, PFV.04, PF4.01, PF4.02, CI2.01, CI2.02, CI2.03, CI3.02 CGE4f, CGE5a |
Knowledge/Understanding Application |
Calculating Interest: Simple and Compound |
|
3 |
EGV.01, EG1.01, EG1.02, EG1.03 CGE2b, CGE2c, CGE3c |
Thinking/Inquiry/Problem Solving Application |
Exploring the Nature of Exponential Growth |
|
4 |
PFV.04, PF4.04, PF4.05 CGE2b, CGE2c |
Thinking/Inquiry/Problem Solving Communication |
Choosing Savings Accounts |
Time: 16 hours
Unit
Description
Students
sketch the graphs of simple exponential functions given their equations, and
compare the rates of change of different types of functions. Emphasis will be
placed on those functions which relate to financial growth through
investigation with technology, the properties of exponential functions with
equations of the form y = ax, and their graphs are
analysed. Students evaluate simple expressions involving natural, rational and
integral exponents, with and without the use of technology. Students perform
operations to solve exponential equations involving common bases.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
EGV.02, EG2.01, EG2.02 CGE4e. CGE5a |
Knowledge/Understanding Thinking/Inquiry/Problem Solving |
Exploring Exponential Functions without technology |
|
2 |
EGV.02, EG2.03 CGE5a, CGE5b |
Communication Thinking/Inquiry/Problem Solving |
Exploring exponential functions using technology |
|
3 |
EGV.03, EG3.01, EG3.02, EG3.03 EG3.04, EG3.05 CGE4e, CGE5a |
Knowledge/Understanding Application |
Manipulating and Solving Exponential Expressions |
Time: 20 hours
Unit
Description
Students
identify terms in a sequence and differentiate between geometric and arithmetic
forms. Relationships between interest calculations and sequences and series are
explored. Using scientific calculators, students solve various problems
involving ordinary annuities and apply this knowledge to investment decisions.
Through investigation and calculation, comparisons are made between investment
alternatives and their associated risks. Students make informed investment
decisions and justify their reasoning for such decisions.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
CIV.01, CI1.01, CI1.02, CI1.03 CGE4e, CGE5a |
Knowledge/Understanding |
Examining Sequences and Series |
|
2 |
CIV.02, CI2.06, CI2.07 CGE4e, CGE5a |
Application |
Applying Sequences and Series to Interest Problems |
|
3 |
CIV.02, CI2.04, CI2.05 CGE5b |
Application Thinking/Inquiry/Problem Solving |
Problem-solving with Annuities |
|
4 |
CIV.03, PFV.04, CI3.03, CI3.04, PF4.03, PF4.04, PF4.05 CGE2b, CGE2c, CGE5e |
Thinking/Inquiry/Problem Solving Communication |
Making Investment Decisions |
Time: 20 hours
Unit
Description
Students
investigate costs and make comparisons among various types of accommodations,
summarizing their findings in presentations. Common mortgage terminology is introduced
and the methods of compounding mortgage interest are explored. Appropriate
technology is used to calculate total interest and to determine the time
required to pay off a mortgage when specific mortgage features are varied
(i.e., payment frequency, amortization period, and payment amounts). Students
use mathematical analysis as a basis for sound accommodation decision-making.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
PFV.02, PFV.04, PF2.01, PF2.02, PF2.03, PF2.04, PF4.01, PF4.02, PF4.03, PF4.04 CGE2b, CGE2c, CGE3c |
Knowledge/ Understanding Communication Thinking/Inquiry/ Problem Solving |
Exploring Accommodation Alternatives |
|
2 |
CIV.03, CI3.05, CI3.06 CGE2b, CGE4f |
Knowledge/ Understanding Thinking/Inquiry/ Problem Solving |
Investigating Mortgage Terminology and Interest Calculations |
|
3 |
CIV.03, CI3.07, CI3.08 CGE5a |
Application |
Developing Amortization Tables |
|
4 |
CIV.03, PFV.04, CI3.09, CI3.10, PF4.05 CGE4f, CGE5a |
Application Thinking/Inquiry/ Problem Solving |
Investigating Mortgage Features |
|
5 |
PFV.02, PFV.04, PF2.02, PF2.03, PF2.04, PF4.03, PF4.04, PF4.05 CGE2b, CGE2c, CGE3c |
Thinking/Inquiry/ Problem Solving Communication |
Making Accommodation Decisions |
Time: 10 hours
Unit
Description
Students
explore and compare the purchasing costs, ownership costs, and features of new
and used vehicles. The financial options of leasing and purchasing vehicles are
investigated and compared. Students collect and analyse information on specific
vehicles and communicate a well-justified decision regarding vehicle and
financing choice.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
PFV.01, PFV.04, PF1.01, PF1.03, PF4.01 CGE4f, CGE5a |
Knowledge/Understanding Communication Thinking/Inquiry/Problem Solving |
Exploring Vehicle Costs |
|
2 |
PFV.01, CIV.03, PF1.02, CI3.13, PF4.01 CGE4f, CGE5a |
Knowledge/Understanding Application |
Comparing Buying vs. Leasing |
|
3 |
PFV.01, PFV.04, CIV.03, PF1.04, PF4.02, PF4.03, PF4.04, PF4.05, CI3.14 CGE2b, CGE2c, CGE3c, CGE5e |
Thinking/Inquiry/Problem Solving Communication |
Making Vehicle Purchase Decisions |
Time: 17 hours
Unit
Description
The
impact of various factors on household budgeting is examined. Students
investigate the impact of types of retailing on the buyer. Currency conversions
are analysed and the impact of foreign exchange rates on the purchases and/or
travel plans of the consumer is considered. This leads to an examination of
credit card/debit card features and the short-term and long-term effects of carrying
credit card debt. Students apply this information, together with the income
potential expected from their chosen career path, to design and justify budgets
for a variety of family groupings. A variety of technological tools, including
spreadsheets and the Internet facilitate explorations in this area.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
PFV.04, PF4.07 CGE5a |
Knowledge/Understanding |
The Impact of Currency Exchange on the Buyer |
|
2 |
PFV.04, PF4.06 CGE5a, CGE4f |
Thinking/Inquiry/Problem Solving |
Investigating the Impact of Selling Techniques on the Buyer |
|
3 |
CIV.03, CI3.11, CI3.12 CGE7b |
Knowledge/Understanding Application |
Investigating the Features of Credit and Debit Cards |
|
4 |
PFV.03, PF3.01, PF3.02, PF3.03 CGE2b, CGE2c, CGE3c |
Thinking/Inquiry/Problem Solving Communication |
Exploring living costs for a Variety of Family Groupings |
|
5 |
PFV.01, PFV.02, PFV.03, PFV.04, PFV.05, PF3.04 CGE2b, CGE2c, CGE3c, CGE5e |
Thinking/Inquiry/Problem Solving Communication |
Designing a Budget Considering Factors Affecting Budget Plans |
Time: 7 hours
Unit
Description
Students
use their chosen career path and the anticipated salary as the basis for the
creation of a realistic long-term financial plan. Specific decisions related to
investments, accommodation choice and vehicle purchases are made in support of
the achievement of specific future goals. Students use the knowledge acquired
throughout the course and appropriate technology to justify their choices.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
CIV.02, CIV.03, PFV.01, PFV.02, PFV.03, PFV.04, CI2.05, CI3.13, CI3.14, PF1.04, PF2.04, PF3.03, PF3.04, PF4.01, PF4.02, PF4.03, PF4.04, PF4.05 CGE3c, CGE4f, CGE4g, CGE5g, CGE7b |
Knowledge/Understanding Application Thinking/Inquiry/Problem Solving Communication |
Financial Planning to Achieve Goal |
The use
of a variety of Teaching/Learning Strategies provides students with multiple
ways to learn the knowledge and skills, and a variety of ways to demonstrate
what they know and can do.
In the use of this Course Profile, teachers should:
·
integrate
the technological tools and software available to promote students’ exploration
and understanding of mathematical concepts;
·
consider
the use of classroom demonstrations in situations where technological tools for
each student are not available, e.g., use of a computer projection device,
sample print-out from spreadsheet applications;
·
invite
guest speakers to enhance the relevancy of course material;
·
make
reference to individual student’s AEPs to establish a realistic framework for
student work in the course;
·
use
a variety of media resources (e.g., newspapers, Internet, magazines)
·
offer
a variety of instructional methods (experimental investigations, use of various
forms of technology, station-based activities, use of visual aids, etc.) to
account for multiple learning styles;
·
provide
opportunities for students to present mathematical results in a variety of
different presentation formats;
·
utilize
a balance of whole-class, small group, and individual instruction through
student-centred and teacher-directed activities.
In achieving the expectations of this course, students:
·
demonstrate
their knowledge and understanding using a variety of methods and
mathematical/technological tools;
·
develop
responsibility for their own learning and decision-making;
·
recognize
the importance of course material as it pertains to their future;
·
increase
their proficiency with technology, particularly as a support for financial
decision-making;
·
become
informed financial decision-makers, aware of the options available to all
consumers;
·
are
able to work individually and cooperatively;
·
summarize
and support decisions using a variety of strategies.
To
effectively evaluate student achievement, a balance of diagnostic, formative,
and summative assessment instruments should be used. Students must be assessed
and evaluated on all learning expectations set out by the curriculum documents.
A variety of assessment tools including observational checklists, performance
criteria, rubrics, the Achievement Chart for Mathematics, marking schemes, and
rating scales. Peer, and self-assessment should be utilized.
Specific
tools which may be considered when evaluating student achievement according to
Achievement Chart categories are provided below. These lists are not
comprehensive, but may serve as a guide for evaluating student achievement.
Achievement
in this category reflects the student’s ability to demonstrate understanding of
mathematical concepts and to perform algorithms.
To evaluate Knowledge/Understanding consider the use of:
·
Quizzes
and daily drills;
·
Short-answer
and skill-based calculations on unit tests and exams;
·
Student-teacher
conferencing;
·
Accuracy
of mathematical answers in reports and presentations.
Achievement
in this category reflects the student’s ability to demonstrate reasoning and to
apply the steps of an inquiry/problem-solving process effectively. This
category lends itself to the use of rubrics due to the open-ended nature of
many of the problems.
To evaluate Thinking/Inquiry/Problem-solving consider the
use of:
·
Broad-based,
open-ended problems on unit tests and exams;
·
Rich
assessment tasks and assignments;
·
Observation
of problem-solving strategies used in group-work;
·
Student-teacher
conferencing;
·
Tasks
requiring complexity of mathematical reasoning in reports and presentations.
Achievement
in this category reflects the student’s ability to apply concepts and
procedures to familiar and unfamiliar settings.
To evaluate Application consider the use of:
·
Appropriate
application of technological tools;
·
Rich
problems on unit tests and exams;
·
Application
of mathematical knowledge and understanding in reports and presentations.
Achievement
in this category reflects the student’s ability to communicate his/her
reasoning using mathematical language, symbols, and conventions. Rubrics are an
effective and efficient tool when evaluating presentations and displays.
To evaluate Communication consider
the use of:
·
Verbal
presentation of homework solutions;
·
Appropriate
use of mathematical language and terminology on tests and assignments;
·
Journals;
·
Use
of visual aids during presentations;
·
Clarity
of written expression in solutions;
·
Observation
of student interaction during group work;
·
Clarity
of mathematical reasoning in reports and presentations.
The
course evaluation must consist of 70% term work and 30% summative assessment.
It is
suggested that students maintain a portfolio to support Unit 8 investigations.
The portfolio could include:
·
Investigation
of career path information (Unit 1)
·
Selection
of appropriate savings options (Unit 2)
·
Description
of investment decisions (Unit 4)
·
Explanation
of accommodation and vehicle choices (Unit 5 and Unit 6)
·
Proposed
personal budget (Unit 7) based on projected income and expenses
Teachers
should be aware that learning skills are not to be included in the
determination of the percentage grade. However, learning skills need to be
assessed and reported separately on the student report cards and should be
tracked throughout the term.
The
following is a partial list of suggested indicators of learning skills:
Organization
·
Preparedness
(materials for class)
·
Submitted
work (including timeliness)
Work
Habits
·
Completion
of homework
·
Use
of class time
Team
Work
·
Cooperation
in group setting
·
Contribution
in group setting
Initiative
·
Display
of leadership
·
Participation
in class discussion
·
Responsibility
for own learning
Works
Independently
·
Commitment
to task
·
Effort
in solving problems individually
Teachers
should refer to the students’ Individual Education Plan (IEP) and consider
their particular learning characteristics to make any necessary accommodations.
Teachers should work in consultation with resource teachers, ESL/ELD teachers,
and parents or guardians to determine appropriate accommodations as they work
through the course to achieve the expectations described in the IEP.
·
Provide
for flexible timelines regarding the completion of projects and assignments.
·
Provide
oral pre-planning of activities with students
·
Allow
students to work in alternate settings (e.g., resource room) where students can
receive assistance with problems
·
Provide
alternate formats for assignments (e.g., written report, oral presentation,
demonstration)
·
Provide
multiple opportunities to be successful on tasks or tests
·
Make
accommodations with respect to test and exam writing environments (e.g., time,
use of technology, use of scribe, etc.)
·
Have
ESL students work in pairs, with peer tutors, with classmates that have the
same linguistic background, or with cooperative supportive groups.
·
Use
peer conferencing to reinforce instructions or information.
·
Ask
an ESL/ELD teacher to review questions, assignments, or assessment instruments.
·
Provide
sets of reference notes, outlines, or critical information, as well as models
of charts, timelines, or diagrams.
·
Reinforce
main ideas by using the think/pair/share peer-assessment strategy.
·
Pair
written instructions with verbal instructions.
·
Use
visuals to illustrate definitions.
·
Simplify
instructions.
·
Highlight
key words or phrases.
·
Brainstorm
in groups using the students’ first language if their usage of English is
limited.
·
Provide
opportunities for students to practice oral presentation skills.
·
Allow
students opportunities to practice oral presentation skills in non-intimidating
environments.
·
Provide
visual or auditory cues.
·
Provide
extensive student-teacher conferencing.
·
Provide
a list of terms (possibly simplified) before an activity begins.
·
Modify
handouts in terms of the terminology and content used, as well as the size and
typeface of the selected font. Allow plenty of space for written responses.
·
Allow
assignments to be completed in alternate formats or using longer timelines.
·
Keep
manipulatives, grid paper, formula sheets, and other aids available for needs
that arise.
·
Contact
parents or guardians for support and suggestions.
·
Provide
the students with oral pre-planning of activities.
Note: The URLs for the websites have been verified by
the writer prior to publication. Given the frequency with which these
designations change, teachers should always verify the websites prior to
assigning them for student use.
Airasian,
P.W. Classroom Assessment.
Andrini,
B. Cooperative Learning and Mathematics: A Multi-Structural Approach.
Baker,
E. “Making Performance Assessment Work: The Road Ahead”. Educational
Leadership 51, (1994):
Burz,
H.L. and K. Marshall. Performance-Based Curriculum for Mathematics.
Bush,
W.S. and A.S. Greer, eds. Mathematics Assessment – A Practical Handbook for
Grades 9-12.
Countryman,
J. Writing to Learn Mathematics.
Hibbard,
K.M., et al. A Teacher’s Guide to Performance-Based Learning and Assessment.
Lambdin,
D.V., et al. Emphasis on Assessment:
National
Council of Teachers of Mathematics. Assessment Standards for School
Mathematics.
OAME,
The Mathematics Gazette.
O’Neil,
J. “Putting Performance Assessment to the Test.” Educational Leadership 49,
8:14-19. 1992.
Romberg,
T.A., ed. Reform in School Mathematics and Authentic Assessment.
Romberg,
T.A., ed. Mathematics Assessment and Evaluation: Imperatives for Mathematics
Educators.
Silver,
E.A., et al. Thinking Through Mathematics: Fostering Inquiry and
Communication in Mathematics Classrooms.
Stepien,
W. and S. Gallagher. “Problem-Based Learning: As Authentic As It Gets.” Educational
Leadership 50, 7:25-28. 1993.
Trafford,
Larry. Educating the Soul: Writing Curriculum for Catholic Secondary Schools.
Career
Information - www.coolmath.com/careers.htm
- http://on.cx.bridges.com
Education
Network of
Internet
Public Library - http://www.ipl.org
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